Basically, the narrow-band vibration or noise produced by an operating device is periodic. This kind of vibration or noise can be formed by the combination of the fundamental frequency and its harmonics. Generally, the fundamental frequency of harmonics is not stable, it is constantly disturbed.
The most widely used algorithm for controlling such periodic vibration and noise is the DXHS (Delayed-X Harmonic Synthesizer). Its outstanding advantage is that it does not require estimating the second path and the convergence is guaranteed. In the meantime, its fatal flaw is that it can't effectively track the fundamental frequency disturbance. The traditional DXHS algorithm is available only for invariant fundamental frequency while extended DXHS has a limited frequency tracking ability.
Meanwhile, even a tiny mismatch in fluctuation frequencies will not only significantly affect DXHS performance, it can even cause instability or divergence. In other words, the control performance of DXHS strongly depends on the proper frequency estimation.
Additionally, all DXHS algorithms only deal with one fundamental frequency. Usually, there are multiple radiation sources with time-variants, this situation corresponds to multiple fundamental frequencies with time-variants.